共查询到20条相似文献,搜索用时 46 毫秒
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Steven G. Krantz 《manuscripta mathematica》1978,24(4):351-378
An intrinsic definition of Lipschitz classes in terms of vector fields on man-ifolds is provided and it is shown that it is locally equivalent with a more classical definition. A finer result is then proved for strongly pseudo-convex CR manifolds and applications of the theorems are given to smoothness of holomorphic functions and estimates for the \(\bar \partial \) and \(\bar \partial _b \) . equations. 相似文献
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Bo Berndtsson 《Journal of Geometric Analysis》1997,7(2):195-215
This paper concernsL ∞-variants of Hörmanders weightedL 2-estimates for the $\bar \partial - equation$ . In particular, we discuss a conjecture concerning suchL ∞-estimates which is related to the corona problem in the ball, and show a weaker version of this conjecture. The proof uses a refinedL 2-estimate for the canonical solution to the $\bar \partial - equation$ . An alternative approach based on von Neumann’s Minimax theorem is also given. 相似文献
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S. Saber 《Mathematica Slovaca》2013,63(3):521-530
For a q-pseudoconvex domain Ω in ? n , 1 ≤ q ≤ n, with Lipschitz boundary, we solve the $\bar \partial $ -problem with exact support in Ω. Moreover, we solve the $\bar \partial $ -problem with solutions smooth up to the boundary over Ω provided that it has smooth boundary. Applications are given to the solvability of the tangential Cauchy-Riemann equations on the boundary. 相似文献
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Steven Bell 《Journal of Geometric Analysis》1993,3(3):195-224
We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz
0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported
away fromz
0 cannot vanish to infinite order atz
0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the
problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in
several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection
and kernel in planar domains.
Research supported by NSF Grant DMS-8922810. 相似文献
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Claudio Rea 《Annali di Matematica Pura ed Applicata》1976,110(1):161-175
Sunto Si dimostra l'esistenza della soluzione per l'operatore di Cauchy-Riemann parametrizzato, nel caso continuo per varietà fortemente
pseudoconvesse e nel caso differenziabile per varietà di Stein.
Entrata in Redazione il 20 maggio 1975.
Supported by C.N.R. research groups. 相似文献
Entrata in Redazione il 20 maggio 1975.
Supported by C.N.R. research groups. 相似文献
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Mats Andersson 《Journal d'Analyse Mathématique》1996,68(1):39-58
LetG
1,…,Gm be bounded holomorphic functions in a strictly pseudoconvex domainD such that
. We prove that for each
(0,q)-form ϕ inL
p(∂D), 1<p<∞, there are
formsu
1, …,u
m inL
p(∂D) such that ΣG
juj=ϕ. This generalizes previous results forq=0. The proof consists in delicate estimates of integral representation formulas of solutions and relies on a certainT1 theorem due to Christ and Journé. For (0,n−1)-forms there is a simpler proof that also gives the result forp=∞. Restricted to one variable this is precisely the corona theorem.
The author was partially supported by the Swedish Natural Research Council. 相似文献
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Let D be a C d q-convex intersection, d ≥ 2, 0 ≤ q ≤ n ? 1, in a complex manifold X of complex dimension n, n ≥ 2, and let E be a holomorphic vector bundle of rank N over X. In this paper, C k -estimates, k = 2, 3,...,∞, for solutions to the \(\bar \partial \)-equation with small loss of smoothness are obtained for E-valued (0, s)-forms on D when n ? q ≤ s ≤ n. In addition, we solve the \(\bar \partial \)-equation with a support condition in C k -spaces. More precisely, we prove that for a \(\bar \partial \)-closed form f in C 0,q k (X D,E), 1 ≤ q ≤ n ? 2, n ≥ 3, with compact support and for ε with 0 < ε < 1 there exists a form u in C 0,q?1 k?ε (X D,E) with compact support such that \(\bar \partial u = f\) in \(X\backslash \bar D\). Applications are given for a separation theorem of Andreotti-Vesentini type in C k -setting and for the solvability of the \(\bar \partial \)-equation for currents. 相似文献
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Giuseppe Zampieri 《Compositio Mathematica》2000,121(2):155-161
For a domain of
we introduce a fairly general and intrinsic condition of weak q-pseudoconvexity, and prove, in Theorem 4, solvability of the
-complex for forms with
-coefficients in degree
. All domains whose boundary have a constant number of negative Levi eigenvalues are easily recognized to fulfill our condition of q-pseudoconvexity; thus we regain the result of Michel (with a simplified proof). Our method deeply relies on the L
2-estimates by Hörmander (with some variants). The main point of our proof is that our estimates (both in weightened-L
2 and in Sobolev norms) are sufficiently accurate to permit us to exploit the technique by Dufresnoy for regularity up to the boundary. 相似文献
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Makhlouf Derridj 《Inventiones Mathematicae》1991,104(1):631-642
Résume Nous étudions des estimations précises pour
sur des hypersurfaces dont la matrice de Levi dans une base a une certaine forme. En particulier, nous donnons, par la méthode de microlocalisation, une démonstration très simple des estimations dites maximales lorsque les valeurs propres sont comparables. Nous obtenons en fait une précision supplémentaire (inégalité 3.17) qui permet de considérer des cas plus généraux. Finalement, de telles estimations, on déduit des estimations sous elliptiques optimales pour
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Oblatum 3-IX-1990 相似文献
Summary We study precise estimates for on hypersurfaces the Levi matrix of which has certain form. In particular, we give and simple proof of the so-called maximal estimates, using the microlocal analysis. In fact, we obtain a refined version (inequality 3.17), which permits the study of more general cases. Finally, from such estimates, we deduce optimal subelliptic estimates for .
Oblatum 3-IX-1990 相似文献